Problem: Simplify the following expression: $k = \dfrac{20f - 20g}{20f + 5} + \dfrac{15f}{20f + 5}$ You can assume $f,g,h \neq 0$.
Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{20f - 20g + 15f}{20f + 5}$ $k = \dfrac{35f - 20g}{20f + 5}$ The numerator and denominator have a common factor of $5$, so we can simplify $k = \dfrac{7f - 4g}{4f + 1}$